[WIP] Rename DeepSeekClient and internal types to provider-neutral types

[Copilot]

• Audit current DeepSeekClient / deepseek_client / deepseek_api_key usage and identify provider-neutral rename targets
• Rename shared client type and engine wiring to provider-neutral names without behavior changes
• Update related docs/comments and active-route API key helper naming where appropriate (keep DeepSeek-specific helpers where truly provider-specific)
• Add/adjust focused tests for renamed helpers and wiring references if needed
• Run targeted tui client/engine/config tests plus grep verification for legacy symbols
• Run security checks (secret scan + CodeQL) and report final status

• Fixes Rename DeepSeekClient / deepseek_client legacy internals to provider-neutral types #5103

[Hmbown]

Triaging this long-stale draft: closing it to keep the board honest. The intent is preserved in #5103 (moved to v0.9.8) — a fresh, smaller PR from current main is very welcome whenever you want to pick it back up.